This book is about only one approach to the subject - loop quantum gravity. It is a subject of considerable technical difficulty, and the literature devoted to it is a formidable one. This feature alone has hindered the cross-fertilization which is, as delineated above, so essential for progress. However, within these pages one will find a much more accessible description of the subject, put forward by one of its leading architects and deepest thinkers. The existence of such a fine book will allow this important subject, quite likely to contribute significantly to the unknown ultimate theory, to be assimilated by a much larger community of the-orists. If this does indeed come to pass, its publication will become one of the most important developments in this very active subfield since its onset.

Foreword, by James Bjorken

Preface

Acknowledgements

Terminology and notation

Part Ⅰ Relativistic foundations

 1 General ideas and heuristic picture

1.1 The problem of quantum gravity

　　1.2 Loop quantum gravity

　　1.3 Conceptual issues

　2 General Relativity

　　2.1 Formalism

　　2.2 The conceptual path to the theory

　　2.3 Interpretation

　　2.4 Complements

　3 Mechanics

　　3.1 Nonrelativistic mechanics: mechanics is about time evolution

　　3.2 Relativistic mechanics

　　3.3 Field theory

　　3.4 Thermal time hypothesis

　4 Hamiltonian general relativity

　　4.1 Einstein-Hamilton-Jacobi

　　4.2 Euclidean GR and real connection

　　4.3 Hamiltonian GR

　5 Quantum mechanics

　　5.1 Nonrelativistic QM

　　5.2 Relativistic QM

　　5.3 Quantum field theory

　　5.4 Quantum gravity

　　5.5 Complements

　　5.6 Relational interpretation of quantum theory

Part Ⅱ 　Loop quantum gravity

 6 Quantum space

　7 Dynamics and matter

　8 Applications

　9 Quantum spacetime: spinfoams

　10 Conclusion

Part Ⅲ　Appendices

Appendxi A Groups and recoupling theory

Reference

Index